Robust Partially Observed Data Sensing via ℓ₂, <i>ₚ</i> Norms With Flexible Adaptive Label Marginal Space for Visual IoT

Visual Internet of Things (VIoT) empowers intelligent sensing by equipping terminal devices with the capability to preliminarily screen and tag sensing data for further processing. However, sensing environments are often imperfect, and partially observed data may be collected at the terminals. This causes several challenges. First, the model fitting process may become oversensitive owing to the presence of varying corrupted data, e.g., continuous occlusion, therefore compromising robustness because of fitting biases. Second, model fitting relies on label information, which consists of fixed and equally spaced categorical variables. Such information cannot adequately reflect the underlying distribution of collected data, as it assumes that each categorical variable is uniformly distributed. This deepens the difficulty of data fitting. To solve the aforementioned problems, this study proposes robust data sensing based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,p}$ </tex-math></inline-formula> norms, where data collected by VIoT terminals can be converted into resilient perceptual data signatures while label information is embedded inside. To deal with the problem stemming from rigid label marginal space, this study introduces an adaptive slack variable to the proposed model. Such a slack variable can automatically adapt itself to sensing data during model fitting while adjusting label marginal space by providing flexible labels. Moreover, a new adaptive regulating mechanism is developed to control the slack variables, such that they can consider multiple coeffects from different loss terms and penalties during optimization, creating error-tolerant soft margins. This is conducive to model fitting, especially for partially observed data. In addition to label slack variables, this study also derives slack variables for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,p}$ </tex-math></inline-formula>-norm loss that is used to capture the nuances of the data, thereby providing flexible Hamming marginal space for resilient signature generation. Experiments on the open datasets show that the proposed method yields better F1 scores than the baselines, improved by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {4.54}\boldsymbol {\%}$ </tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {8.08}\boldsymbol {\%}$ </tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {6.02}\boldsymbol {\%}$ </tex-math></inline-formula>, with respect to various data corruption, including impulse noise, continuous occlusion, and missing values. Such results verify the effectiveness of the proposed method.